Libraries and shortcuts

library(plyr)
library(afex)
library(ggplot2)
library(reshape)
library(data.table)

read_data <- function(directory, separator=","){
  x <- data.frame()
  for(i in list.files(directory)){
    i_dat <- read.delim(paste(directory,"/",i, sep = ""), comment.char="#", sep=separator, header=T)
    x <- rbind(x, i_dat)
  }
  return(x)
}

num <- function(x){
  as.numeric(as.character(x))
}

IES <- function(dat, FUN="mean"){
  dat$rt <- num(dat$rt)
  dat$correct <- num(dat$correct)
  if(FUN=="mean"){
    dat$ies <- mean(dat$rt, na.rm = T) / mean(dat$correct, na.rm = T)
  } else if(FUN=="median"){
    dat$ies <- median(dat$rt, na.rm = T) / mean(dat$correct, na.rm = T)
  }
  return(dat)
}

t_report <- function(ttest){
  if(ttest$p.value[[1]] < 0.001){
    p <- ", p < 0.001"
  }else{
    p <- paste0(", p = ", as.character(round(ttest$p.value[[1]], digits = 3)))
  }
  paste0("t(", ttest$parameter[[1]], ") = ", round(ttest$statistic[[1]], digits = 2), p)
}

bars <- stat_summary(fun.y=mean, geom="bar", position = position_dodge())
errorbars <-  stat_summary(fun.data="mean_se", geom="errorbar",position=position_dodge(width=0.10),width=0.2) 
errorbars2 <-  stat_summary(fun.data="mean_se", geom="errorbar",position=position_dodge(width=0.90),width=0.2) 
points <- stat_summary(fun.y=mean, geom="point")
lines <- stat_summary(fun.y=mean, geom="line")
x_ax <- scale_x_continuous(breaks = c(1,2,8,9))
reg <- geom_smooth(method = lm, se=F)
hline <- geom_hline(yintercept = 0)
vline <- geom_vline(xintercept = 0)

cohens_dz <- function(ttest, do_print = F){
  dz <- abs(as.numeric(ttest[[1]])/sqrt(as.numeric(ttest[[2]]+1)))
  if (do_print){
    print(paste0("Cohen's dz = ", round(dz, 2)))
  } else {
    return(dz)
  }
  
}

layout <- theme_bw() + theme(axis.text = element_text(size = 26), 
                              axis.title=element_text(size=24, face = "bold"),
                              strip.text = element_text(size=18, face = "bold"), 
                              strip.background = element_rect(fill="white"),
                              rect = element_rect(fill = "transparent"),
                              plot.background = element_rect(fill = "transparent", color = NA),
                              title = element_text(size= 22, face="bold"))

layout2 <- theme_bw() + theme(axis.text = element_text(size = 16), 
                              axis.title=element_text(size=20, face = "bold"),
                              # legend.position = "top",
                              legend.text = element_text(size=9),
                              legend.title = element_text(size=10, face="bold"),
                              strip.text = element_text(size=10, face = "bold"), 
                              strip.background = element_rect(fill="white"),
                              legend.position = "none")

read data

snas <- read.csv2("snas.csv")
snas <- snas[snas$training=="experiment",]

errors_sna <- ddply(snas, .(subject_id), function(x) 
  data.frame(n_correct_catch=length(x[x$correct==1 & x$catch==1,]$correct), 
             n_correct_noncatch=length(x[x$correct==1 & x$catch==0,]$correct),  
             n_incorrect_catch=length(x[x$correct==-1,]$correct), 
             n_incorrect_noncatch=length(x[x$correct==0,]$correct)))

errorrate_catch <- length(snas[snas$correct==-1&snas$catch==1,]$correct) / length(snas[snas$correct%in%c(-1,1) & snas$catch==1,]$correct)
errorrate_noncatch <- length(snas[snas$correct==0&snas$catch==0,]$correct) / length(snas[snas$correct%in%c(0,1) & snas$catch==0,]$correct)

answers <- read.csv2("answers.csv")
snas <- merge(snas, answers, by="subject_id")
snas <- snas[snas$language != "nongerman",]

errors_sna$errorrate_catch <- errors_sna$n_incorrect_catch / (errors_sna$n_incorrect_catch+errors_sna$n_correct_catch)
errors_sna$errorrate_noncatch <- errors_sna$n_incorrect_noncatch / (errors_sna$n_incorrect_noncatch+errors_sna$n_correct_noncatch)


too_many_errors_SNA <- errors_sna[which(errors_sna$errorrate_catch > mean(errors_sna$errorrate_catch) + 3*sd(errors_sna$errorrate_catch)),]$subject_id

snas$target <- num(snas$target)

## Warning in num(snas$target): NAs durch Umwandlung erzeugt

snas$position_index <- num(snas$position_index)

## Warning in num(snas$position_index): NAs durch Umwandlung erzeugt

snas$rt <- num(snas$rt)

## Warning in num(snas$rt): NAs durch Umwandlung erzeugt

snarc <- read.csv2("snarc.csv")
#during training
# snarc <- snarc[snarc$training=="training" & snarc$block==-1,]
#during experiment
snarc <- snarc[snarc$training == "experiment",]

snarc <- merge(snarc, answers, by="subject_id")

snarc <- snarc[snarc$language != "nongerman",]

# "correct" values:
# -999: middle button pressed
# -6: too slow (response)
# -5: too slow (release)
# -1: wrong dimension
print(paste("any incorrect responses: ", as.character(length(snarc[snarc$correct!=1,]$correct))))

## [1] "any incorrect responses:  409"

print(paste("wrong dimension: ", as.character(length(snarc[snarc$correct==-1,]$correct))))

## [1] "wrong dimension:  168"

print(paste("correct dimension, wrong button: ", as.character(length(snarc[snarc$correct==0,]$correct))))

## [1] "correct dimension, wrong button:  204"

print(paste("too slow (release or response): ", as.character(length(snarc[snarc$correct%in%c(-5, -6),]$correct))))

## [1] "too slow (release or response):  27"

print(paste("other error (middle button pressed): ", as.character(length(snarc[snarc$correct==-999,]$correct))))

## [1] "other error (middle button pressed):  10"

errors_snarc <- ddply(snarc, .(subject_id), function(x) 
  data.frame(n_correct=length(x[x$correct==1,]$correct), 
             n_incorrect=length(x[x$correct!=1,]$correct)))

errors_snarc$errorrate <- errors_snarc$n_incorrect / (errors_snarc$n_incorrect+errors_snarc$n_correct)

too_many_errors_snarc <- errors_snarc[which(errors_snarc$errorrate > mean(errors_snarc$errorrate) + 3*sd(errors_snarc$errorrate)),]$subject_id

mini_dat <- read.csv2("mini_dat.csv")
mini_dat <- mini_dat[mini_dat$training == "experiment",]

mini_dat$rt <- num(mini_dat$rt)

## Warning in num(mini_dat$rt): NAs durch Umwandlung erzeugt

mini_dat <- merge(mini_dat, answers, by="subject_id")

mini_dat <- mini_dat[mini_dat$language=="german",]

print(paste("any incorrect responses: ", as.character(length(mini_dat[mini_dat$correct!=1,]$correct))))

## [1] "any incorrect responses:  90"

print(paste("too slow: ", as.character(length(mini_dat[mini_dat$correct==-1,]$correct))))

## [1] "too slow:  12"

print(paste("wrong button: ", as.character(length(mini_dat[mini_dat$correct==0,]$correct))))

## [1] "wrong button:  78"

errors_mini_dat <- ddply(mini_dat, .(subject_id), function(x) 
  data.frame(n_correct=length(x[x$correct==1,]$correct), 
             n_incorrect=length(x[x$correct!=1,]$correct)))

errors_mini_dat$errorrate <- errors_mini_dat$n_incorrect / (errors_mini_dat$n_incorrect+errors_mini_dat$n_correct)

too_many_errors_mini_dat <- errors_mini_dat[which(errors_mini_dat$errorrate > mean(errors_mini_dat$errorrate) + 3*sd(errors_mini_dat$errorrate)),]$subject_id

snas <- snas[!snas$subject_id %in% too_many_errors_SNA & !snas$subject_id %in% too_many_errors_snarc & !snas$subject_id %in% too_many_errors_mini_dat,]
snarc <- snarc[!snarc$subject_id %in% too_many_errors_SNA & !snarc$subject_id %in% too_many_errors_snarc & !snarc$subject_id %in% too_many_errors_mini_dat,]
mini_dat <- mini_dat[!mini_dat$subject_id %in% too_many_errors_SNA & !mini_dat$subject_id %in% too_many_errors_snarc & !mini_dat$subject_id %in% too_many_errors_mini_dat,]

overall RTs

s1 <- aggregate(data=snas, rt~subject_id+target,mean)
s2 <- aggregate(data=snarc, rt~subject_id+target,mean)
s3 <- aggregate(data=mini_dat, rt~subject_id+target,mean)
s1$experiment <- "2d_sna"
s2$experiment <- "2d_snarc"
s3$experiment <- "1d_snarc"

ggplot(rbind(s1, s2, s3), aes(target, rt, colour=experiment)) + points + lines + errorbars + layout + scale_x_continuous(breaks = c(1, 2, 8, 9))

preparations 2D SNA (Experiment 1)

snas <- snas[snas$correct != -1,]

sna_noncatch <- snas[snas$catch == 0,]

sna_noncatch$side_position <- ifelse(sna_noncatch$position_index < 5, 1,
                                     ifelse(sna_noncatch$position_index < 10, 2,
                                            ifelse(sna_noncatch$position_index < 15, 3,
                                                   ifelse(sna_noncatch$position_index < 20, 4,5))))

sna_noncatch$side <- factor(sna_noncatch$side_position, labels=c("far_left", "left", "right", "far_right"))

sna_noncatch$generalside <- factor(ifelse(sna_noncatch$position_index < 10, 1,
                                     ifelse(sna_noncatch$position_index < 15, 2,
                                            3)),
                              labels=c("left", "right"))

sna_noncatch$vert_position <- (sna_noncatch$position_index %% 5) + 1
sna_noncatch$vert <- factor(sna_noncatch$vert_position, labels = c("far_down", "down", "up", "far_up"))

sna_noncatch$generalvert <- factor(ifelse(sna_noncatch$position_index %% 5 %in% c(0, 1), 1,
                                     ifelse(sna_noncatch$position_index %% 5 == 2, 2,
                                            3)),
                              labels=c("down", "up"))

sna_noncatch$distance_from_middle <- ifelse(sna_noncatch$position_index == 12, 0, 
                                            ifelse(sna_noncatch$position_index %in% c(6:8,11,13,16:18), 1, 
                                                   ifelse(sna_noncatch$position_index %in% c(0:5,9,10,14,15,19:24), 2, 99)))

sna_noncatch$size_factor <- factor(ifelse(sna_noncatch$target < 5, 1, 2), labels = c("small", "large"))
sna <- sna_noncatch

data_agg <- ddply(sna, .(target, vert, side), summarize, mRT = mean(rt, na.rm=T), mER = 1-mean(correct, na.rm=T))
# no speed-accuracy tradeoff:
cor.test(data_agg$mRT, data_agg$mER)

## 
##  Pearson's product-moment correlation
## 
## data:  data_agg$mRT and data_agg$mER
## t = 5.0363, df = 62, p-value = 4.366e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3377434 0.6928616
## sample estimates:
##       cor 
## 0.5388197

snarcy_hor_general_pre <- data.table(sna)[, .(ies=mean(rt, na.rm = T) / mean(correct, na.rm = T)), by=.(subject_id, generalside, target)]
snarcy_vert_general_pre <- data.table(sna)[, .(ies=mean(rt, na.rm = T) / mean(correct, na.rm = T)), by=.(subject_id, generalvert, target)]

snarcy_hor_general <- merge(snarcy_hor_general_pre[snarcy_hor_general_pre$generalside == "left",], snarcy_hor_general_pre[snarcy_hor_general_pre$generalside=="right",], by=c("subject_id", "target"))
snarcy_hor_general$RminusL <- snarcy_hor_general$ies.y - snarcy_hor_general$ies.x
snarcy_vert_general <- merge(snarcy_vert_general_pre[snarcy_vert_general_pre$generalvert == "down",], snarcy_vert_general_pre[snarcy_vert_general_pre$generalvert=="up",], by=c("subject_id", "target"))
snarcy_vert_general$UminusD <- snarcy_vert_general$ies.y - snarcy_vert_general$ies.x

snarcy_hor_general_slopes <- ddply(snarcy_hor_general, .(subject_id), function(x) coef(lm(RminusL ~ target, data=x)))
snarcy_vert_general_slopes <- ddply(snarcy_vert_general, .(subject_id), function(x) coef(lm(UminusD ~ target, data=x)))


##original rt
snarcy_hor_general_pre_rt <- aggregate(data=sna, rt ~ subject_id + generalside + target, mean)
snarcy_vert_general_pre_rt <- aggregate(data=sna, rt ~ subject_id + generalvert + target, mean)

snarcy_hor_general_rt <- merge(snarcy_hor_general_pre_rt[snarcy_hor_general_pre_rt$generalside == "left",],
                               snarcy_hor_general_pre_rt[snarcy_hor_general_pre_rt$generalside=="right",], by=c("subject_id", "target"))
snarcy_hor_general_rt$RminusL <- snarcy_hor_general_rt$rt.y - snarcy_hor_general_rt$rt.x
snarcy_vert_general_rt <- merge(snarcy_vert_general_pre_rt[snarcy_vert_general_pre_rt$generalvert == "down",],
                                snarcy_vert_general_pre_rt[snarcy_vert_general_pre_rt$generalvert=="up",], by=c("subject_id", "target"))
snarcy_vert_general_rt$UminusD <- snarcy_vert_general_rt$rt.y - snarcy_vert_general_rt$rt.x

snarcy_hor_general_slopes_rt <- ddply(snarcy_hor_general_rt, .(subject_id), function(x) coef(lm(RminusL ~ target, data=x)))
snarcy_vert_general_slopes_rt <- ddply(snarcy_vert_general_rt, .(subject_id), function(x) coef(lm(UminusD ~ target, data=x)))

Prelim analyses

ggplot(sna, aes(side, rt)) + points + errorbars + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

ggplot(sna, aes(target, rt, colour=side)) + points + lines + errorbars + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

ggplot(sna, aes(vert, rt)) + points + errorbars + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

ggplot(sna, aes(target, rt, colour=vert)) + points + lines + errorbars + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

ggplot(sna, aes(size_factor, rt, fill = generalside)) + bars + errorbars2 + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

ggplot(sna, aes(size_factor, rt, fill = generalvert)) + bars + errorbars2 + layout

## Warning: Removed 81 rows containing non-finite values (stat_summary).

## Warning: Removed 81 rows containing non-finite values (stat_summary).

#RT general
ddply(sna, .(generalside), summarize, M=mean(rt, na.rm=T), SD=sd(rt, na.rm=T))

##   generalside        M       SD
## 1        left  993.573 445.1189
## 2       right 1033.629 469.2166

ddply(sna, .(generalvert), summarize, M=mean(rt, na.rm=T), SD=sd(rt, na.rm=T))

##   generalvert         M       SD
## 1        down 1076.8269 453.3306
## 2          up  950.3505 453.4368

side_rts <- aggregate(data=sna, rt ~ subject_id + generalside, mean)
t.test(side_rts$rt ~ side_rts$generalside, paired=T)

## 
##  Paired t-test
## 
## data:  side_rts$rt by side_rts$generalside
## t = -3.1363, df = 42, p-value = 0.003122
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -65.56745 -14.22439
## sample estimates:
## mean of the differences 
##               -39.89592

cohens_dz(t.test(side_rts$rt ~ side_rts$generalside, paired=T), T)

## [1] "Cohen's dz = 0.48"

vert_rts <- aggregate(data=sna, rt ~ subject_id + generalvert, mean)
t.test(vert_rts$rt ~ vert_rts$generalvert, paired=T)

## 
##  Paired t-test
## 
## data:  vert_rts$rt by vert_rts$generalvert
## t = 5.7774, df = 42, p-value = 8.3e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   82.20125 170.45711
## sample estimates:
## mean of the differences 
##                126.3292

cohens_dz(t.test(vert_rts$rt ~ vert_rts$generalvert, paired=T), T)

## [1] "Cohen's dz = 0.88"

#RT
ddply(sna, .(distance_from_middle), summarize, M=round(mean(rt, na.rm=T)), SD=round(sd(rt, na.rm=T)))

##   distance_from_middle    M  SD
## 1                    1  753 325
## 2                    2 1101 462

sna_dist <- aggregate(data=sna, rt ~ subject_id + distance_from_middle, mean)
t.test(sna_dist$rt ~ sna_dist$distance_from_middle, paired=T)

## 
##  Paired t-test
## 
## data:  sna_dist$rt by sna_dist$distance_from_middle
## t = -29.701, df = 42, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -372.0418 -324.7003
## sample estimates:
## mean of the differences 
##               -348.3711

cohens_dz(t.test(sna_dist$rt ~ sna_dist$distance_from_middle, paired=T), T)

## [1] "Cohen's dz = 4.53"

#size
ddply(sna, .(size_factor), summarize, M=mean(rt, na.rm=T), SD=sd(rt, na.rm=T))

##   size_factor         M       SD
## 1       small  936.5168 407.3745
## 2       large 1091.0577 491.3090

size_rts <- aggregate(data=sna, rt ~ subject_id + size_factor, mean)
t.test(size_rts$rt ~ size_rts$size_factor, paired = T)

## 
##  Paired t-test
## 
## data:  size_rts$rt by size_rts$size_factor
## t = -11.299, df = 42, p-value = 2.588e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -182.6454 -127.2890
## sample estimates:
## mean of the differences 
##               -154.9672

cohens_dz(t.test(size_rts$rt ~ size_rts$size_factor, paired = T), T)

## [1] "Cohen's dz = 1.72"

General SNA(RC)

The SNARC effect usually describes faster left side (or spatially lower) responses for small numbers and right side (or spatially upper) responses for large numbers. In this experiment, there was only one response button, but target numbers were presented at different locations in 2D space. Therefore, instead of response locations, we examined presentation locations. We therefore originally expected faster responses for small numbers when presented on the left side and/or in lower space (i.e., lower half of the screen) and for large number when presented on the right side and/or in upper space (i.e., upper half of the screen). In this study we found evidence for this only for the vertical dimension and we expected to find approximately the same in the present study.

ggplot(snarcy_hor_general, aes(target, RminusL)) +
  points +
  reg +
  x_ax +
  hline +
  coord_cartesian(ylim=c(-150, 75)) +
  labs(title="Horizontal 2D SNA", x = "Target number", y = "dIES (right - left) in ms") +
  layout

# ggsave("sna_hor_poster.png", width = 7, height = 5.5, units='in', dpi=600, bg="transparent")

t_hor_ies <- t.test(snarcy_hor_general_slopes$target, mu = 0)
t_hor_ies

## 
##  One Sample t-test
## 
## data:  snarcy_hor_general_slopes$target
## t = 3.662, df = 42, p-value = 0.0006946
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##   4.070315 14.063628
## sample estimates:
## mean of x 
##  9.066971

t_report(t_hor_ies)

## [1] "t(42) = 3.66, p < 0.001"

cohens_dz(t_hor_ies, T)

## [1] "Cohen's dz = 0.56"

ggplot(snarcy_hor_general_rt, aes(target, RminusL)) + 
  points + 
  reg + 
  x_ax + 
  layout + 
  hline + 
  #coord_cartesian(ylim=c(-120, 100)) + 
  ylab("RT (right - left) in ms") + 
  xlab("Target number")

t_hor_rt <- t.test(snarcy_hor_general_slopes_rt$target, mu = 0)
t_hor_rt

## 
##  One Sample t-test
## 
## data:  snarcy_hor_general_slopes_rt$target
## t = 3.6093, df = 42, p-value = 0.0008113
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##   3.874615 13.702745
## sample estimates:
## mean of x 
##   8.78868

t_report(t_hor_rt)

## [1] "t(42) = 3.61, p < 0.001"

cohens_dz(t_hor_rt, T)

## [1] "Cohen's dz = 0.55"

ggplot(snarcy_vert_general, aes(target, UminusD)) +
  points +
  reg +
  x_ax +
  hline +
  coord_cartesian(ylim=c(-150, 75)) +
  ylab("dIES (top - bottom) in ms") +
  xlab("Target number") +
  labs(title="Vertical 2D SNA" ) +
  layout

# ggsave("sna_vert_poster.png", width = 7, height = 5.5, units='in', dpi=600, bg="transparent")
t_vert_ies <- t.test(snarcy_vert_general_slopes$target, mu = 0)
t_vert_ies

## 
##  One Sample t-test
## 
## data:  snarcy_vert_general_slopes$target
## t = -2.0728, df = 42, p-value = 0.04437
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -9.3769341 -0.1253915
## sample estimates:
## mean of x 
## -4.751163

t_report(t_vert_ies)

## [1] "t(42) = -2.07, p = 0.044"

cohens_dz(t_vert_ies, T)

## [1] "Cohen's dz = 0.32"

ggplot(snarcy_vert_general_rt, aes(target, UminusD)) + 
  points + 
  reg + 
  x_ax + 
  layout + 
  hline + 
  #coord_cartesian(ylim=c(-120, 100)) + 
  ylab("RT (top - bottom) in ms") + 
  xlab("Target number")

t_vert_rt <- t.test(snarcy_vert_general_slopes_rt$target, mu = 0)
t_vert_rt

## 
##  One Sample t-test
## 
## data:  snarcy_vert_general_slopes_rt$target
## t = -1.9971, df = 42, p-value = 0.05232
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -9.11749697  0.04773205
## sample estimates:
## mean of x 
## -4.534882

t_report(t_vert_rt)

## [1] "t(42) = -2, p = 0.052"

cohens_dz(t_vert_rt, T)

## [1] "Cohen's dz = 0.3"

compare_slopes <- t.test(snarcy_hor_general_slopes$target, snarcy_vert_general_slopes$target, paired = T)
compare_slopes

## 
##  Paired t-test
## 
## data:  snarcy_hor_general_slopes$target and snarcy_vert_general_slopes$target
## t = 3.9853, df = 42, p-value = 0.0002631
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   6.820927 20.815341
## sample estimates:
## mean of the differences 
##                13.81813

cohens_dz(compare_slopes, T)

## [1] "Cohen's dz = 0.61"

compare_rt_slopes <- t.test(snarcy_hor_general_slopes_rt$target, snarcy_vert_general_slopes_rt$target, paired = T)
compare_rt_slopes

## 
##  Paired t-test
## 
## data:  snarcy_hor_general_slopes_rt$target and snarcy_vert_general_slopes_rt$target
## t = 3.8624, df = 42, p-value = 0.000382
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   6.362074 20.285051
## sample estimates:
## mean of the differences 
##                13.32356

cohens_dz(compare_rt_slopes, T)

## [1] "Cohen's dz = 0.59"

Hor*Vert Here, we tested whether individuals with weaker/stronger horizontal SNAs tended to have weaker/stronger vertical SNAs, respecitvely. However, we found no evidence for that.

slopes_ies <- merge(snarcy_hor_general_slopes, snarcy_vert_general_slopes, by="subject_id")
slopes_ies$Horizontal <- slopes_ies$target.x
slopes_ies$Vertical <- slopes_ies$target.y

ggplot(slopes_ies, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2 +
  labs(title = "2D SNA slopes (IES)")

ggplot(slopes_ies, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2 + reg +
  labs(title = "2D SNA slopes (IES)")#+

  #coord_cartesian(xlim=c(-20,20), ylim=c(-20, 20))

slopes_ies$Hor <- ifelse(slopes_ies$Horizontal < 0, "snarc", "reverse")
slopes_ies$Vert <- ifelse(slopes_ies$Vertical < 0, "snarc", "reverse")
ddply(slopes_ies, .(Hor), summarize, n = length(subject_id))

##       Hor  n
## 1 reverse 32
## 2   snarc 11

ddply(slopes_ies, .(Vert), summarize, n = length(subject_id))

##      Vert  n
## 1 reverse 18
## 2   snarc 25

ddply(slopes_ies, .(Hor,Vert), summarize, n = length(subject_id))

##       Hor    Vert  n
## 1 reverse reverse 15
## 2 reverse   snarc 17
## 3   snarc reverse  3
## 4   snarc   snarc  8

cor.test(slopes_ies$Horizontal, slopes_ies$Vertical)

## 
##  Pearson's product-moment correlation
## 
## data:  slopes_ies$Horizontal and slopes_ies$Vertical
## t = -0.36023, df = 41, p-value = 0.7205
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3505993  0.2483637
## sample estimates:
##         cor 
## -0.05617013

slopes <- merge(snarcy_hor_general_slopes_rt, snarcy_vert_general_slopes_rt, by="subject_id")
slopes$Horizontal <- slopes$target.x
slopes$Vertical <- slopes$target.y

ggplot(slopes, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2 +
  labs(title = "2D SNA slopes (RTs)")

ggplot(slopes, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2 + reg +
  labs(title = "2D SNA slopes (RTs)") #+

  #coord_cartesian(xlim=c(-20,20), ylim=c(-20, 20))

slopes$Hor <- ifelse(slopes$Horizontal < 0, "snarc", "reverse")
slopes$Vert <- ifelse(slopes$Vertical < 0, "snarc", "reverse")
ddply(slopes, .(Hor), summarize, n = length(subject_id))

##       Hor  n
## 1 reverse 31
## 2   snarc 12

ddply(slopes, .(Vert), summarize, n = length(subject_id))

##      Vert  n
## 1 reverse 17
## 2   snarc 26

ddply(slopes, .(Hor,Vert), summarize, n = length(subject_id))

##       Hor    Vert  n
## 1 reverse reverse 14
## 2 reverse   snarc 17
## 3   snarc reverse  3
## 4   snarc   snarc  9

cor.test(slopes$Horizontal, slopes$Vertical)

## 
##  Pearson's product-moment correlation
## 
## data:  slopes$Horizontal and slopes$Vertical
## t = -0.47242, df = 41, p-value = 0.6391
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3658390  0.2318885
## sample estimates:
##         cor 
## -0.07357997

preparations 2D SNARC (Experiment 2)

snarc_complete <- snarc
snarc <- snarc[snarc$correct==1,]

snarc$size <- factor(ifelse(snarc$target < 5, 1, 2), labels = c("small", "large"))
snarc$parity <- factor(ifelse(snarc$target%%2==0, 1, 2), labels=c("even", "odd"))
snarc$button <- factor(ifelse(snarc$pressed_button == "b'le'", 1, ifelse(snarc$pressed_button == "b'ri'", 2, ifelse(snarc$pressed_button == "b'do'", 3, ifelse(snarc$pressed_button=="b'up'", 4, 9)))), labels = c("left", "right", "down", "up"))

pre-visualizations

ggplot(snarc, aes(target, rt)) + lines + points + errorbars + x_ax + layout

ggplot(snarc, aes(target, rt, colour=dimension)) + lines + points + errorbars + x_ax + layout

ggplot(snarc, aes(parity, rt, colour=button, fill=button)) + bars + errorbars + facet_wrap(~dimension, ncol = 4) + layout

ggplot(snarc, aes(parity, rt, colour=dimension, fill=dimension)) + bars + errorbars + layout

ggplot(snarc, aes(target, rt, colour=button)) + lines + points + errorbars + x_ax + layout

ggplot(snarc, aes(as.integer(target>5), rt, colour=button)) + lines + points + errorbars +  layout + scale_x_continuous(breaks = c(0, 1), labels = c("small", "large")) + labs(x = "target size")

#reaction time (rt)
ggplot(snarc, aes(button, rt)) + points + errorbars + layout

“pre-rt”: part of rt from target presentation until release of central button (pre-reaction time)

ggplot(snarc, aes(button, pre_rt)) + points + errorbars + layout

“mt” (movement time): part of rt from release of central button until press of response button (movement time)

ggplot(snarc, aes(button, mt)) + points + errorbars + layout

horizontal

snarc_hor <- snarc[snarc$dimension=="horizontal",]
snarc_hor$side <- snarc_hor$button
snarc_hor$congruency <- factor(ifelse((snarc_hor$side == "left" & snarc_hor$size == "small") | (snarc_hor$side == "right" & snarc_hor$size == "large"), 1, 2), labels = c("congruent", "incongruent"))

ggplot(snarc_hor, aes(congruency, rt)) + points + errorbars + layout

ggplot(snarc_hor, aes(side, rt, colour=congruency)) + points + errorbars + layout

ggplot(snarc_hor, aes(target, rt, colour=congruency, shape=side)) + lines + stat_summary(fun.y=mean, geom="point", size=4) + errorbars + layout + x_ax

ps_agg <- aggregate(data=snarc_hor, rt ~ subject_id + target + side, mean)
ps_agg_snarc <- merge(ps_agg[ps_agg$side=="left",], ps_agg[ps_agg$side=="right",], by=c("subject_id", "target"))
ps_agg_snarc$dRT <- ps_agg_snarc$rt.y - ps_agg_snarc$rt.x

ggplot(ps_agg_snarc, aes(target, dRT)) + points + reg + layout + x_ax + hline + labs(x = "Target number", y = "dRT (right - left) in ms", title = "Horizontal 2D SNARC") + coord_cartesian(ylim = c(-60, 20))

# ggsave("snarc_hor_poster.png", units = "in", width = 7, height = 5.5, dpi = 600, bg="transparent")

ggplot(snarc_hor, aes(congruency, mt)) + points + errorbars + layout

ggplot(snarc_hor, aes(side, mt, colour=congruency)) + points + errorbars + layout

ggplot(snarc_hor, aes(target, mt, colour=congruency, shape=side)) + lines + stat_summary(fun.y=mean, geom="point", size=4) + errorbars + layout + x_ax

ps_agg_mt <- aggregate(data=snarc_hor, mt ~ subject_id + target + side, mean)
ps_agg_snarc_mt <- merge(ps_agg_mt[ps_agg_mt$side=="left",], ps_agg_mt[ps_agg_mt$side=="right",], by=c("subject_id", "target"))
ps_agg_snarc_mt$dMT <- ps_agg_snarc_mt$mt.y - ps_agg_snarc_mt$mt.x

ggplot(ps_agg_snarc_mt, aes(target, dMT)) + points + reg + errorbars + layout + x_ax

slopes_mt <- ddply(ps_agg_snarc_mt, .(subject_id), function(x) coef(lm(dMT ~ target, data=x)))
t.test(slopes_mt$target, mu=0)

## 
##  One Sample t-test
## 
## data:  slopes_mt$target
## t = -1.2936, df = 42, p-value = 0.2029
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -6.336590  1.386245
## sample estimates:
## mean of x 
## -2.475173

vertical

snarc_vert <- snarc[snarc$dimension=="vertical",]
snarc_vert$vert <- snarc_vert$button
snarc_vert$congruency <- factor(ifelse((snarc_vert$vert == "down" & snarc_vert$size == "small") | (snarc_vert$vert == "up" & snarc_vert$size == "large"), 1, 2), labels = c("congruent", "incongruent"))

ggplot(snarc_vert, aes(congruency, rt)) + points + errorbars + layout

ggplot(snarc_vert, aes(vert, rt, colour=congruency)) + points + errorbars + layout

ggplot(snarc_vert, aes(target, rt, colour=congruency, shape=vert)) + lines + stat_summary(fun.y=mean, geom="point", size=4) + errorbars + layout + x_ax

ps_agg_v <- aggregate(data=snarc_vert, rt ~ subject_id + target + vert, mean)
ps_agg_snarc_v <- merge(ps_agg_v[ps_agg_v$vert=="down",], ps_agg_v[ps_agg_v$vert=="up",], by=c("subject_id", "target"))
ps_agg_snarc_v$dRT <- ps_agg_snarc_v$rt.y - ps_agg_snarc_v$rt.x

ggplot(ps_agg_snarc_v, aes(target, dRT)) + points + reg + x_ax + layout + hline + labs(x = "Target number", y = "dRT (top - bottom) in ms", title = "Vertical 2D SNARC") + coord_cartesian(ylim = c(-60, 20))

# ggsave("snarc_vert_poster.png", units = "in", width = 7, height = 5.5, dpi = 600, bg="transparent")

snarc_slopes_hor <- ddply(ps_agg_snarc, .(subject_id), function(x) coef(lm(dRT ~ target, data=x)))
snarc_slopes_vert <- ddply(ps_agg_snarc_v, .(subject_id), function(x) coef(lm(dRT ~ target, data=x)))

t.test(snarc_slopes_hor$target, mu=0)

## 
##  One Sample t-test
## 
## data:  snarc_slopes_hor$target
## t = -0.50539, df = 42, p-value = 0.6159
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -6.097818  3.655344
## sample estimates:
## mean of x 
## -1.221237

t_report(t.test(snarc_slopes_hor$target, mu=0))

## [1] "t(42) = -0.51, p = 0.616"

cohens_dz(t.test(snarc_slopes_hor$target, mu=0), T)

## [1] "Cohen's dz = 0.08"

t.test(snarc_slopes_vert$target, mu=0)

## 
##  One Sample t-test
## 
## data:  snarc_slopes_vert$target
## t = -0.15866, df = 42, p-value = 0.8747
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -8.052795  6.878867
## sample estimates:
##  mean of x 
## -0.5869639

t_report(t.test(snarc_slopes_vert$target, mu=0))

## [1] "t(42) = -0.16, p = 0.875"

cohens_dz(t.test(snarc_slopes_vert$target, mu=0), T)

## [1] "Cohen's dz = 0.02"

t.test(snarc_slopes_hor$target, snarc_slopes_vert$target, paired = T)

## 
##  Paired t-test
## 
## data:  snarc_slopes_hor$target and snarc_slopes_vert$target
## t = -0.14007, df = 42, p-value = 0.8893
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -9.772426  8.503880
## sample estimates:
## mean of the differences 
##               -0.634273

slopes_rc <- merge(snarc_slopes_hor, snarc_slopes_vert, by="subject_id")
slopes_rc$Horizontal <- slopes_rc$target.x
slopes_rc$Vertical <- slopes_rc$target.y

ggplot(slopes_rc, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2# +

  #coord_cartesian(xlim=c(-20,20), ylim=c(-20, 20))
ggplot(slopes_rc, aes(Horizontal, Vertical)) + 
  geom_point(size=2.5) + 
  hline + 
  vline + 
  layout2 +
  reg# +

  #coord_cartesian(xlim=c(-20,20), ylim=c(-20, 20))

cor.test(slopes_rc$Horizontal, slopes_rc$Vertical)

## 
##  Pearson's product-moment correlation
## 
## data:  slopes_rc$Horizontal and slopes_rc$Vertical
## t = -0.35105, df = 41, p-value = 0.7273
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3493432  0.2497063
## sample estimates:
##         cor 
## -0.05474318

preparations 1D SNARC (Experiment 3)

print(paste("any incorrect responses: ", as.character(length(mini_dat[mini_dat$correct!=1,]$correct))))

## [1] "any incorrect responses:  67"

print(paste("too slow: ", as.character(length(mini_dat[mini_dat$correct==-1,]$correct))))

## [1] "too slow:  11"

print(paste("wrong button: ", as.character(length(mini_dat[mini_dat$correct==0,]$correct))))

## [1] "wrong button:  56"

mini_dat <- mini_dat[mini_dat$correct==1,]

mini_dat$side <- factor(ifelse(mini_dat$pressed_button=="b'le'", 1, ifelse(mini_dat$pressed_button=="b'ri", 2, 9)), labels = c("left", "right"))
ddply(mini_dat, .(side), summarise, M=mean(rt), SD=sd(rt))

##    side        M       SD
## 1  left 789.6270 177.6681
## 2 right 778.4642 186.5272

ggplot(mini_dat, aes(target, rt)) + bars + errorbars + x_ax + layout

ggplot(mini_dat, aes(target, rt, colour=side)) + points + lines + errorbars + x_ax + layout

mini_dat$size <- factor(ifelse(mini_dat$target < 5, 1, 2), labels = c("small", "large"))
mini_dat$congruency <- factor(ifelse((mini_dat$side == "left" & mini_dat$size == "small") | (mini_dat$side == "right" & mini_dat$size == "large"), 1, 2), labels = c("congruent", "incongruent"))

snarc

pm_agg <- aggregate(data=mini_dat, rt ~ subject_id + target + side, mean)
pm_agg_snarc <- merge(pm_agg[pm_agg$side=="left",], pm_agg[pm_agg$side=="right",], by=c("subject_id", "target"))
pm_agg_snarc$dRT <- pm_agg_snarc$rt.y - pm_agg_snarc$rt.x

ggplot(pm_agg_snarc, aes(target, dRT)) + points + reg + x_ax + hline + labs(x = "Target number", y = "dRT (right - left) in ms", title = "1D SNARC") + coord_cartesian(ylim = c(-60, 20)) + layout

# ggsave("minisnarc_poster.png", units = "in", width = 7, height = 5.5, dpi = 600, bg="transparent")

minisnarc_slopes <- ddply(pm_agg_snarc, .(subject_id), function(x) coef(lm(dRT ~ target, data=x)))
t.test(minisnarc_slopes$target, mu=0)

## 
##  One Sample t-test
## 
## data:  minisnarc_slopes$target
## t = -2.6048, df = 42, p-value = 0.01266
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -9.476459 -1.202783
## sample estimates:
## mean of x 
## -5.339621

t_report(t.test(minisnarc_slopes$target, mu=0))

## [1] "t(42) = -2.6, p = 0.013"

cohens_dz(t.test(minisnarc_slopes$target, mu=0), T) 

## [1] "Cohen's dz = 0.4"

1D SNARC * 2D SNARC (horizontal)

data_from_multisnarc <- snarc_slopes_hor
data_from_multisnarc$slope_multi_hor <- data_from_multisnarc$target
minisnarc_slopes$slope_mini <- minisnarc_slopes$target
merged_data <- merge(minisnarc_slopes, data_from_multisnarc, by="subject_id")
ggplot(merged_data, aes(slope_multi_hor, slope_mini)) + points + hline + vline + reg + labs(x="Horizontal slopes from 2D SNARC", y = "Slopes from 1D SNARC", subtitle = "Correlation horizontal 2D & 1D SNARC") + layout

# ggsave(filename = "Mini_Multi_correlation.png", width = 7, height = 5.5, dpi = 600, units = "in", bg="transparent")
cor.test(merged_data$slope_mini, merged_data$slope_multi_hor)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_data$slope_mini and merged_data$slope_multi_hor
## t = 1.7943, df = 41, p-value = 0.08014
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.03320787  0.52742781
## sample estimates:
##       cor 
## 0.2698272

merged_mini_multiMT <- merge(minisnarc_slopes, slopes_mt, by="subject_id")
merged_mini_multiMT$multi_MT_hor <- merged_mini_multiMT$target.y
ggplot(merged_mini_multiMT, aes(multi_MT_hor, slope_mini)) + points + hline + vline + reg + layout + labs(x="Horizontal slopes 2D SNARC - Movement Time", y = "Slopes from 1D SNARC")

cor.test(merged_mini_multiMT$slope_mini, merged_mini_multiMT$multi_MT_hor)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_mini_multiMT$slope_mini and merged_mini_multiMT$multi_MT_hor
## t = 2.8099, df = 41, p-value = 0.007563
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1154243 0.6265621
## sample estimates:
##       cor 
## 0.4018376

1D SNARC * 2D SNARC (vertical)

v_data_from_multisnarc <- snarc_slopes_vert
v_data_from_multisnarc$slope_multi_vert <- v_data_from_multisnarc$target
merged_data_v <- merge(minisnarc_slopes, v_data_from_multisnarc, by="subject_id")
ggplot(merged_data_v, aes(slope_multi_vert, slope_mini)) + points + hline + vline + reg + labs(x="Vertical slopes from 2D SNARC", y = "Slopes from 1D SNARC") + layout

# ggsave(filename = "Mini_MultiVert_correlation.png", width = 7, height = 5.5, dpi = 600, units = "in", bg="transparent")

cor.test(merged_data_v$slope_mini, merged_data_v$slope_multi_vert)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_data_v$slope_mini and merged_data_v$slope_multi_vert
## t = -0.0079194, df = 41, p-value = 0.9937
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3014687  0.2992182
## sample estimates:
##        cor 
## -0.0012368

1D SNARC * 2D SNA (horizontal)

sna_hor_slopes_from_other <- snarcy_hor_general_slopes
sna_hor_slopes_from_other$sna_slope_hor <- sna_hor_slopes_from_other$target
minisnarc_slopes$minisnarc_slope <- minisnarc_slopes$target
merged_sna_mini <- merge(minisnarc_slopes, sna_hor_slopes_from_other, by="subject_id")
ggplot(merged_sna_mini, aes(sna_slope_hor, minisnarc_slope)) + points + hline + vline + reg + labs(x="Horizontal slopes from 2D SNA", y = "Slopes from 1D SNARC", subtitle = "Correlation horizontal SNA & 1D SNARC") + layout

# ggsave(filename = "Mini_SNA_correlation.png", width = 7, height = 5.5, dpi = 600, units = "in", bg="transparent")

cor.test(merged_sna_mini$sna_slope_hor, merged_sna_mini$minisnarc_slope)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_sna_mini$sna_slope_hor and merged_sna_mini$minisnarc_slope
## t = -0.76665, df = 41, p-value = 0.4477
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.4047724  0.1881819
## sample estimates:
##        cor 
## -0.1188811

1D SNARC * 2D SNA (vertical)

sna_vert_slopes_from_other <- snarcy_vert_general_slopes
sna_vert_slopes_from_other$sna_slope_vert <- sna_vert_slopes_from_other$target
merged_snaV_mini <- merge(minisnarc_slopes, sna_vert_slopes_from_other, by="subject_id")
ggplot(merged_snaV_mini, aes(sna_slope_vert, minisnarc_slope)) + points + hline + vline + reg + labs(x="Vertical slopes from 2D SNA", y = "Slopes from 1D SNARC", subtitle = "Correlation vertical SNA & 1D SNARC") + layout

# ggsave(filename = "Mini_SNAvert_correlation.png", width = 7, height = 5.5, dpi = 600, units = "in", bg="transparent")

cor.test(merged_snaV_mini$sna_slope_vert, merged_snaV_mini$minisnarc_slope)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_snaV_mini$sna_slope_vert and merged_snaV_mini$minisnarc_slope
## t = -1.9049, df = 41, p-value = 0.06383
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.53930041  0.01662493
## sample estimates:
##        cor 
## -0.2851427

2D SNA * 2D SNARC (horizontal)

sna_hor_slopes_from_other <- snarcy_hor_general_slopes
sna_hor_slopes_from_other$sna_slope_hor <- sna_hor_slopes_from_other$target
snarc_slopes_hor$snarc_slope_hor <- snarc_slopes_hor$target
merged_data_sna_snarc <- merge(sna_hor_slopes_from_other, snarc_slopes_hor, by="subject_id")
ggplot(merged_data_sna_snarc, aes(sna_slope_hor, snarc_slope_hor)) + points + hline + vline + reg + layout + labs(x="Horizontal slopes 2D SNA", y = "Horizontal slopes 2D SNARC")

cor.test(merged_data_sna_snarc$sna_slope_hor, merged_data_sna_snarc$snarc_slope_hor)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_data_sna_snarc$sna_slope_hor and merged_data_sna_snarc$snarc_slope_hor
## t = -0.43519, df = 41, p-value = 0.6657
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3608049  0.2373689
## sample estimates:
##         cor 
## -0.06780919

2D SNA * 2D SNARC (vertical)

sna_vert_slopes_from_other <- snarcy_vert_general_slopes
sna_vert_slopes_from_other$sna_slope_vert <- sna_vert_slopes_from_other$target
snarc_slopes_vert$snarc_slope_vert <- snarc_slopes_vert$target
merged_data_sna_snarc_v <- merge(sna_vert_slopes_from_other, snarc_slopes_vert, by="subject_id")
ggplot(merged_data_sna_snarc_v, aes(sna_slope_vert, snarc_slope_vert)) + points + hline + vline + reg + layout + labs(x="Vertical slopes 2D SNA", y = "Vertical slopes 2D SNARC")

cor.test(merged_data_sna_snarc_v$sna_slope_vert, merged_data_sna_snarc_v$snarc_slope_vert)

## 
##  Pearson's product-moment correlation
## 
## data:  merged_data_sna_snarc_v$sna_slope_vert and merged_data_sna_snarc_v$snarc_slope_vert
## t = -0.41223, df = 41, p-value = 0.6823
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3576888  0.2407422
## sample estimates:
##         cor 
## -0.06424702

“task switching”

We did not find evidence for a horizontal nor vertical SNARC effect in the 2D SNARC paradigm. Our best guess so far is that spatial-numerical associations did not manifest on a trial-to-trial basis, but need more time to take effect. That is, switching between the two dimensions might have weakended spatial-numerical associations. In exploratory analyses we therefore also addressed potential effects of these switches between dimensions (or rather, of staying within the same dimension for two or more trials).

taskswitch <- function(df){
  df$switched <- NA
  df$switched_i <- 0
  for(i in df$trial){
    if(i > 0){
      df[df$trial == i,]$switched <- ifelse(df[df$trial == i,]$dimension == df[df$trial == i-1,]$dimension, 0, 1)
      df[df$trial == i,]$switched_i <- ifelse(df[df$trial == i,]$dimension == df[df$trial == i-1,]$dimension, df[df$trial==i-1,]$switched_i + 1, 0)
    } else{
      df[df$trial == i,]$switched_i <- 0

    }
  }
  return(df)
}

snarc_switch <- ddply(snarc_complete, .(subject_id, block), taskswitch)
snarc_switch$switched <- factor(snarc_switch$switched, labels = c("repeated dimension", "switched dimension"))
snarc_switch <- snarc_switch[snarc_switch$correct==1,]
snarc_switch$size <- factor(ifelse(snarc_switch$target < 5, 1, 2), labels = c("small", "large"))
snarc_switch$parity <- factor(ifelse(snarc_switch$target%%2==0, 1, 2), labels=c("even", "odd"))
snarc_switch_hor <- snarc_switch[snarc_switch$dimension=="horizontal",]
snarc_switch_hor$side <- factor(ifelse(snarc_switch_hor$pressed_button == "b'le'", 1, 2), labels = c("left", "right"))
snarc_switch_hor$congruency <- factor(ifelse((snarc_switch_hor$side == "left" & snarc_switch_hor$size == "small") | (snarc_switch_hor$side == "right" & snarc_switch_hor$size == "large"), 1, 2), labels = c("congruent", "incongruent"))
snarc_switch_vert <- snarc_switch[snarc_switch$dimension=="vertical",]
snarc_switch_vert$vert <- factor(ifelse(snarc_switch_vert$pressed_button == "b'do'", 1, 2), labels = c("down", "up"))
snarc_switch_vert$congruency <- factor(ifelse((snarc_switch_vert$vert == "down" & snarc_switch_vert$size == "small") | (snarc_switch_vert$vert == "up" & snarc_switch_vert$size == "large"), 1, 2), labels = c("congruent", "incongruent"))

horizontal_per_switching

ps_agg_s <- aggregate(data=snarc_switch_hor, rt ~ subject_id + switched + target + side, mean)
ps_agg_snarc_s <- merge(ps_agg_s[ps_agg_s$side=="left",], ps_agg_s[ps_agg_s$side=="right",], by=c("subject_id", "target", "switched"))
ps_agg_snarc_s$dRT <- ps_agg_snarc_s$rt.y - ps_agg_snarc_s$rt.x

ggplot(ps_agg_snarc_s, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~switched)

horizontal_per_multiple_switching

ps_agg_s_mult <- aggregate(data=snarc_switch_hor, rt ~ subject_id + switched_i + target + side, mean)
ps_agg_snarc_s_mult <- merge(ps_agg_s_mult[ps_agg_s_mult$side=="left",], ps_agg_s_mult[ps_agg_s_mult$side=="right",], by=c("subject_id", "target", "switched_i"))
ps_agg_snarc_s_mult$dRT <- ps_agg_snarc_s_mult$rt.y - ps_agg_snarc_s_mult$rt.x

ggplot(ps_agg_snarc_s_mult, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~switched_i)

## Warning: Removed 3 rows containing missing values (geom_errorbar).

# ggplot(ps_agg_snarc, aes(target, dRT)) + points + reg + facet_wrap(~subject_id)

ps_agg_snarc_s_mult$switched_med <- ifelse(ps_agg_snarc_s_mult$switched_i %in% c(1,2), "once_or_twice", ifelse(ps_agg_snarc_s_mult$switched_i%in% c(3,4), "thrice_or_fource", NA))
slopes_switched_med <- ddply(ps_agg_snarc_s_mult[!is.na(ps_agg_snarc_s_mult$switched_med),], .(subject_id, switched_med), function(x) coef(lm(dRT ~ target, data=x)))
slopes_switched_i <- ddply(ps_agg_snarc_s_mult, .(subject_id, switched_i), function(x) coef(lm(dRT ~ target, data=x)))



ggplot(slopes_switched_i, aes(switched_i, target)) + bars + errorbars

## Warning: Removed 33 rows containing non-finite values (stat_summary).

## Warning: Removed 33 rows containing non-finite values (stat_summary).

## Warning: Removed 1 rows containing missing values (geom_errorbar).

ggplot(slopes_switched_med, aes(switched_med, target)) + bars + errorbars

## Warning: Removed 12 rows containing non-finite values (stat_summary).

## Warning: Removed 12 rows containing non-finite values (stat_summary).

for (i in c(0:3)){
  print(t_report(t.test(slopes_switched_i[slopes_switched_i$switched_i==i,]$target, mu = 0)))
}

## [1] "t(42) = -0.11, p = 0.909"
## [1] "t(42) = 0.22, p = 0.825"
## [1] "t(38) = -0.81, p = 0.425"
## [1] "t(11) = 0.74, p = 0.473"

horizontal_per_multiple_switching_MOVEMENT_TIME

ps_agg_s <- aggregate(data=snarc_switch_hor, mt ~ subject_id + switched_i + target + side, mean)
ps_agg_snarc_s_mt <- merge(ps_agg_s[ps_agg_s$side=="left",], ps_agg_s[ps_agg_s$side=="right",], by=c("subject_id", "target", "switched_i"))
ps_agg_snarc_s_mt$dMT <- ps_agg_snarc_s_mt$mt.y - ps_agg_snarc_s_mt$mt.x

ggplot(ps_agg_snarc_s_mt, aes(target, dMT)) + points + reg + errorbars + facet_wrap(~switched_i)

## Warning: Removed 3 rows containing missing values (geom_errorbar).

# ggplot(ps_agg_snarc, aes(target, dMT)) + points + reg + facet_wrap(~subject_id)

ps_agg_snarc_s_mt$switched_med <- ifelse(ps_agg_snarc_s_mt$switched_i %in% c(1,2), "once_or_twice", ifelse(ps_agg_snarc_s_mt$switched_i%in% c(3,4), "thrice_or_fource", NA))
slopes_switched_med <- ddply(ps_agg_snarc_s_mt[!is.na(ps_agg_snarc_s_mt$switched_med),], .(subject_id, switched_med), function(x) coef(lm(dMT ~ target, data=x)))
slopes_switched_i <- ddply(ps_agg_snarc_s_mt, .(subject_id, switched_i), function(x) coef(lm(dMT ~ target, data=x)))



ggplot(slopes_switched_i, aes(switched_i, target)) + bars + errorbars

## Warning: Removed 33 rows containing non-finite values (stat_summary).

## Warning: Removed 33 rows containing non-finite values (stat_summary).

## Warning: Removed 1 rows containing missing values (geom_errorbar).

ggplot(slopes_switched_med, aes(switched_med, target)) + bars + errorbars

## Warning: Removed 12 rows containing non-finite values (stat_summary).

## Warning: Removed 12 rows containing non-finite values (stat_summary).

for (i in c(0:3)){
  print(t_report(t.test(slopes_switched_i[slopes_switched_i$switched_i==i,]$target, mu = 0)))
}

## [1] "t(42) = 0.55, p = 0.587"
## [1] "t(42) = -0.54, p = 0.592"
## [1] "t(38) = -1.06, p = 0.296"
## [1] "t(11) = 1.25, p = 0.238"

horizontal_per_mapping

snarc_switch_hor$horizontal_mappings <- ifelse(snarc_switch_hor$mapping %in% c("left_down_odd", "right_down_odd"), "down_odd", "up_odd")
ps_agg_m <- aggregate(data=snarc_switch_hor, rt ~ subject_id + horizontal_mappings + target + side, mean)
ps_agg_snarc_m <- merge(ps_agg_m[ps_agg_m$side=="left",], ps_agg_m[ps_agg_m$side=="right",], by=c("subject_id", "target", "horizontal_mappings"))
ps_agg_snarc_m$dRT <- ps_agg_snarc_m$rt.y - ps_agg_snarc_m$rt.x

ps_agg_snarc_m_slopes <- ddply(ps_agg_snarc_m, .(subject_id, horizontal_mappings), function(x) coef(lm(dRT ~ target, data=x)))
t.test(ps_agg_snarc_m_slopes[ps_agg_snarc_m_slopes$horizontal_mappings=="down_odd",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_m_slopes[ps_agg_snarc_m_slopes$horizontal_mappings ==     "down_odd", ]$target
## t = -1.1091, df = 42, p-value = 0.2737
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -13.001885   3.779247
## sample estimates:
## mean of x 
## -4.611319

t.test(ps_agg_snarc_m_slopes[ps_agg_snarc_m_slopes$horizontal_mappings=="up_odd",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_m_slopes[ps_agg_snarc_m_slopes$horizontal_mappings ==     "up_odd", ]$target
## t = 0.58706, df = 42, p-value = 0.5603
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -4.559397  8.300287
## sample estimates:
## mean of x 
##  1.870445

ggplot(ps_agg_snarc_m, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~horizontal_mappings)

vertical_per_switching

ps_agg_v_s <- aggregate(data=snarc_switch_vert, rt ~ subject_id + switched + target + vert, mean)
ps_agg_snarc_v_s <- merge(ps_agg_v_s[ps_agg_v_s$vert=="down",], ps_agg_v_s[ps_agg_v_s$vert=="up",], by=c("subject_id", "target", "switched"))
ps_agg_snarc_v_s$dRT <- ps_agg_snarc_v_s$rt.y - ps_agg_snarc_v_s$rt.x


ps_agg_snarc_v_s_slopes <- ddply(ps_agg_snarc_v_s, .(subject_id, switched), function(x) coef(lm(dRT ~ target, data=x)))
t.test(ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched=="repeated dimension",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched == "repeated dimension",     ]$target
## t = 0.76846, df = 42, p-value = 0.4465
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -6.756014 15.065344
## sample estimates:
## mean of x 
##  4.154665

t.test(ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched=="switched dimension",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched == "switched dimension",     ]$target
## t = -1.5724, df = 42, p-value = 0.1234
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -16.955156   2.104588
## sample estimates:
## mean of x 
## -7.425284

t.test(ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched=="repeated dimension",]$target, ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched=="switched dimension",]$target, paired = T)

## 
##  Paired t-test
## 
## data:  ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched == "repeated dimension",  and ps_agg_snarc_v_s_slopes[ps_agg_snarc_v_s_slopes$switched == "switched dimension",     ]$target and     ]$target
## t = 1.7042, df = 42, p-value = 0.09573
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.132822 25.292719
## sample estimates:
## mean of the differences 
##                11.57995

ggplot(ps_agg_snarc_v_s, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~switched)

# ggplot(ps_agg_snarc_v, aes(target, dRT)) + points + reg + facet_wrap(~subject_id)

vertical_per_multiple_switching

ps_agg_s_v_i <- aggregate(data=snarc_switch_vert, rt ~ subject_id + switched_i + target + vert, mean)
ps_agg_snarc_s_v <- merge(ps_agg_s_v_i[ps_agg_s_v_i$vert=="down",], ps_agg_s_v_i[ps_agg_s_v_i$vert=="up",], by=c("subject_id", "target", "switched_i"))
ps_agg_snarc_s_v$dRT <- ps_agg_snarc_s_v$rt.y - ps_agg_snarc_s_v$rt.x

ggplot(ps_agg_snarc_s_v, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~switched_i)

## Warning: Removed 2 rows containing missing values (geom_errorbar).

# ggplot(ps_agg_snarc, aes(target, dRT)) + points + reg + facet_wrap(~subject_id)

ps_agg_snarc_s_v$switched_med <- ifelse(ps_agg_snarc_s_v$switched_i %in% c(1), 1, ifelse(ps_agg_snarc_s_v$switched_i%in% c(2,3), 2, NA))
slopes_switched_med <- ddply(ps_agg_snarc_s_v[!is.na(ps_agg_snarc_s_v$switched_med),], .(subject_id, switched_med), function(x) coef(lm(dRT ~ target, data=x)))
slopes_switched_i <- ddply(ps_agg_snarc_s_v, .(subject_id, switched_i), function(x) coef(lm(dRT ~ target, data=x)))



ggplot(slopes_switched_i, aes(switched_i, target)) + bars + errorbars

## Warning: Removed 31 rows containing non-finite values (stat_summary).

## Warning: Removed 31 rows containing non-finite values (stat_summary).

ggplot(slopes_switched_med, aes(switched_med, target)) + bars + errorbars

vertical_per_multiple_switching_MOVEMENT_TIME

ps_agg_s_v_i <- aggregate(data=snarc_switch_vert, mt ~ subject_id + switched_i + target + vert, mean)
ps_agg_snarc_s_v <- merge(ps_agg_s_v_i[ps_agg_s_v_i$vert=="down",], ps_agg_s_v_i[ps_agg_s_v_i$vert=="up",], by=c("subject_id", "target", "switched_i"))
ps_agg_snarc_s_v$dMT <- ps_agg_snarc_s_v$mt.y - ps_agg_snarc_s_v$mt.x

ggplot(ps_agg_snarc_s_v, aes(target, dMT)) + points + reg + errorbars + facet_wrap(~switched_i)

## Warning: Removed 2 rows containing missing values (geom_errorbar).

# ggplot(ps_agg_snarc, aes(target, dMT)) + points + reg + facet_wrap(~subject_id)

ps_agg_snarc_s_v$switched_med <- ifelse(ps_agg_snarc_s_v$switched_i %in% c(1), 1, ifelse(ps_agg_snarc_s_v$switched_i%in% c(2,3), 2, NA))
slopes_switched_med <- ddply(ps_agg_snarc_s_v[!is.na(ps_agg_snarc_s_v$switched_med),], .(subject_id, switched_med), function(x) coef(lm(dMT ~ target, data=x)))
slopes_switched_i <- ddply(ps_agg_snarc_s_v, .(subject_id, switched_i), function(x) coef(lm(dMT ~ target, data=x)))



ggplot(slopes_switched_i, aes(switched_i, target)) + bars + errorbars

## Warning: Removed 31 rows containing non-finite values (stat_summary).

## Warning: Removed 31 rows containing non-finite values (stat_summary).

ggplot(slopes_switched_med, aes(switched_med, target)) + bars + errorbars

vertical_per_mapping

snarc_switch_vert$vertical_mappings <- ifelse(snarc_switch_vert$mapping %in% c("left_down_odd", "left_up_odd"), "left_odd", "right_odd")
ps_agg_m_v <- aggregate(data=snarc_switch_vert, rt ~ subject_id + vertical_mappings + target + vert, mean)
ps_agg_snarc_m_v <- merge(ps_agg_m_v[ps_agg_m_v$vert=="down",], ps_agg_m_v[ps_agg_m_v$vert=="up",], by=c("subject_id", "target", "vertical_mappings"))
ps_agg_snarc_m_v$dRT <- ps_agg_snarc_m_v$rt.y - ps_agg_snarc_m_v$rt.x

ps_agg_snarc_m_v_slopes <- ddply(ps_agg_snarc_m_v, .(subject_id, vertical_mappings), function(x) coef(lm(dRT ~ target, data=x)))
t.test(ps_agg_snarc_m_v_slopes[ps_agg_snarc_m_v_slopes$vertical_mappings=="left_odd",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_m_v_slopes[ps_agg_snarc_m_v_slopes$vertical_mappings ==     "left_odd", ]$target
## t = 0.67266, df = 42, p-value = 0.5048
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -5.927065 11.853691
## sample estimates:
## mean of x 
##  2.963313

t.test(ps_agg_snarc_m_v_slopes[ps_agg_snarc_m_v_slopes$vertical_mappings=="right_odd",]$target, mu=0)

## 
##  One Sample t-test
## 
## data:  ps_agg_snarc_m_v_slopes[ps_agg_snarc_m_v_slopes$vertical_mappings ==     "right_odd", ]$target
## t = -0.82287, df = 42, p-value = 0.4152
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -13.353770   5.618035
## sample estimates:
## mean of x 
## -3.867868

ggplot(ps_agg_snarc_m_v, aes(target, dRT)) + points + reg + errorbars + facet_wrap(~vertical_mappings)

Setup of Experiment 1 (2D SNA)

2D SNA (Experiment 1)

Setup of Experiment 2 (2D SNARC)

2D SNARC (Experiment 2)

The same button board was used for Experiment 3 (1D SNARC). However, only the leftmost and rightmost button were used and participants were asked to use their left and right index finger, respectively, to press the buttons.

Procedure of Experiment 1 (2D SNA)

Procedure 2D SNA (Experiment 1)

Auditory stimuli (and target stimuli) were 1, 2, 8, and 9. (“Neun” is German for “nine”.)

Instruction sheet of Experiment 2

Instruction sheet 2D SNARC (Experiment 2)

Colour codes were balanced between participants (i.e., yellow or blue for horizontally or vertically aligned buttons). Each participant absoved each of the four possible parity-to-position mappings. (“gerade” and “ungerade” is German for “even” and “odd”, respectively.)

Instruction sheet of Experiment 3

Instruction sheet 1D SNARC (Experiment 3)

Each participant absolved each of the two possible parity-to-position mappings.(“gerade” and “ungerade” is German for “even” and “odd”, respectively.)